1. 3x ≤ 9
Divide 3 on both sides.
3/3 = 1 9/3 = 3
x ≤ 1
Your line graph should have a little line like this: | and with the number 1 under it.
It will be a shaded in circle since it's greater than, less than, and you goes to infinite.
2. 4x - 3 ≥ 13
Add 3 to both sides
4x ≥ 16
divide 4 into both sides
x ≥ 4
3. 4x - 3 < 13
same thing as 2
add 3 onto both sides
4x < 16
x < 4
this one is a bit different when you are using a line graph, you are going to do a opened circle, do not shade it in and then draw back.
4. 5x + 10 > 14x - 8
add 8 onto both sides.
5x + 18 > 14x
subtract 5x.
18 > 9x
x > 9
5. 2x - 6 < 2
add 6 to both sides
2x < 8
divide by 2,
x < 4
6. 2x - 5 ≤ x - 2
add to onto both sides.
2x - 3 ≤ x
subtract x onto both sides
-3 ≤ -x
This is crucial, any time you are dividing by a negative number you will always flip the sign.
x ≥ 3
7. 3x - 14 ≥ 2 - 5x
add 5x on both sides
8x - 14 ≥ 2
add 14 on both sides
8x ≥ 16
divide both sides by 8
x ≥ 2
I will let you do the last 3 on your own, but I hope you got the overall gist of it.
